The cosmic distance duality relation ( CDDR ) has been test through several astronomical observations in the last years .
This relation establishes a simple equation relating the angular diameter ( D _ { A } ) and luminosity ( D _ { L } ) distances at a redshift z , D _ { L } D _ { A } ^ { -1 } ( 1 + z ) ^ { -2 } = \eta = 1 .
However , only very recently this relation has been observationally tested at high redshifts ( z \approx 3.6 ) by using luminosity distances from type Ia supernovae ( SNe Ia ) and gamma ray bursts ( GRBs ) plus angular diameter distances from strong gravitational lensing ( SGL ) observations .
The results show that no significant deviation from the CDDR validity has been verified .
In this work , we test the potentialities of future luminosity distances from gravitational waves ( GWs ) sources to impose limit on possible departures of CDDR jointly with current SGL observations .
The basic advantage of D _ { L } from GWs is being insensitive to non-conservation of the number of photons .
By simulating 600 , 900 and 1200 data of GWs using the Einstein Telescope ( ET ) as reference , we derive limits on \eta ( z ) function and obtain that the results will be at least competitive with current limits from the SNe Ia + GRBs + SGLs analyses .